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Introduction to Probability Theory: With Contemporary Applications Hardcover – July, 1996

ISBN-13: 978-0716730231 ISBN-10: 0716730235

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Product Details

  • Hardcover: 351 pages
  • Publisher: W H Freeman & Co (Sd) (July 1996)
  • Language: English
  • ISBN-10: 0716730235
  • ISBN-13: 978-0716730231
  • Product Dimensions: 0.8 x 7.5 x 9.5 inches
  • Shipping Weight: 1.8 pounds
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #3,505,866 in Books (See Top 100 in Books)

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Format: Paperback Verified Purchase
I bought this book for my students because the level is perfect. I wanted a treatment that assumed a non-trivial background in analysis and methods of proof and rigor.

But in my opinion this book really hasn't made it out of the beta-testing phase yet. There are just so many confusing treatments of material and less than enlightening approaches.

In section 1.2 the concept of the limit of the relative frequency of successes in a repeated experiment is called an "empirical law" and it is said that the law can no more be proved that Newton's law of cooling. Talk about confusing, no beginning student understands what to make of that comment. Why not just say as long as this limit exists and always converges to the same number, then we can consistently call that number the probability of A.

Then section 1.2 introduces the concept of calculating probabilities using a formula that only works if outcomes are equally likely. Without pointing this concept of outcomes being "equally likely" out in this section the student is left inadequately prepared to understand what they are doing. Section 1.5 is called the equally likely case, but that really starts in section 1.2 with equation (1.4) and so needs to be pointed out there. In short, the concept of a sample space of equally likely outcomes would do a lot to clarify the exposition in section 1.2.

Another example of the rough state of the exposition is the definition of sigma-algebra. It is given with the condition that omega itself is in the set. But this follows from unions and complements so should not be included it should be deduced. Then the basic fact that an algebra is also closed under intersections is never stated or proven in the exposition but is subsequently simply assumed.
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Format: Hardcover Verified Purchase
Excellent explanations. Not too wordy. Great for someone fairly new to probability who wants to learn it at a college level. It is not as advanced as some texts, but it does build up to using calculus.

I've taken 3 semesters of calculus and read some very basic algebra based probability booklets, and I find this book to be perfect for me.
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